Chapter_2 - a a ) ( ) ( t t a v t v x + Area of rectangle...

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Ch 2: Kinematics in One Dimension Focus: Position (x), Velocity (v), Acceleration (a) x(t) as area under v(t), v(t) as area under a(t) Catch- up, crash! O Reference frame Origin Scale Meters x t Clock Seconds Characterizing Motion Position varies with time Newton (1642-1727) Witchcraft! Apple attracted to Earth: Attraction might extend to the moon!
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Ch 2: Kinematics in One Dimension O x t 1 Velocity (m/sec) 2 2 1 2 1 2 t t x x t x x v = = Average Velocity: (slope of chord) x t Instantaneous Velocity: (slope of curve) 0 as = t dt dx v x Newton: “Fluxions”
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Ch 2: Kinematics in One Dimension O v x t 1 Instantaneous Acceleration: (slope of curve) 0 as = t dt dv a x x Acceleration (m/sec 2 ) 2 2 1 2 1 2 t t v v t v x a x x x = = Average Acceleration: (slope of chord) v x t
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Ch 2: Kinematics in One Dimension = + = t t t n x n x x n t a t t v t v 0 ) ( ) ( ) ( 0 Velocity as Area under Acceleration vs Time Curve a x (t) t t 0 t 2 t 1 t n-1 t n t ) ( t a t v x x = Integral = Area under curve + t t x x t a dt v t v 0 ) ' ( ' ) ( 0 Newton: “Fluents”
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Ch 2: Kinematics in One Dimension Velocity as Area under Acceleration vs Time Curve a x (t) t t 0 t Example: Constant acceleration
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Unformatted text preview: a a ) ( ) ( t t a v t v x + Area of rectangle Ch 2: Kinematics in One Dimension = + = t t t n x n n t v t t x t x ) ( ) ( ) ( Position as Area under Velocity vs Time Curve v x (t) t t t 2 t 1 t n-1 t n Integral = Area under curve + t t x t v dt x t x ) ' ( ' ) ( t ) ( t v t x x = Ch 2: Kinematics in One Dimension Position as Area under Velocity vs Time Curve ) ( t t a v v + = t t v t v a (t-t ) Triangle Rectangle Example: Constant a 2 2 1 ) ( ) ( ) ( t t a t t v x t x + + = Rectangle + Triangle Ch 2: Kinematics in One Dimension a v v t t = ) ( 2 2 2 x x a v v + = For constant acceleration a , initial position x , initial velocity v : 2 2 1 ) ( ) ( t t a t t v x x + + = ) ( t t a v v + = Memorize this! Memorize this!...
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Chapter_2 - a a ) ( ) ( t t a v t v x + Area of rectangle...

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